randRange( 2, 10 ) randRangeNonZero( -10, 10 ) randRange( 2, 10 ) randRangeNonZero( 2, 10 ) fractionReduce( D - B, A - C ) randFromArray([ "<", ">", "≤", "≥" ]) { "<": ">", ">": "<", "≤": "≥", "≥": "≤" }[ REL ]

Solve for x:

Ax + B REL Cx + D

x A - C > 0 ? REL : FREL ( D - B ) / ( A - C )

Subtract Cx from both sides:

(Ax + B) - Cx REL (Cx + D) - Cx

A - Cx + B REL D

B > 0 ? "Subtract" : "Add" abs(B) B > 0 ? "from" : "to" both sides:

(A - Cx + B) + -B REL D + -B

A - Cx REL D - B

Divide both sides by A - C. Because A - C is positive, the inequality sign REL should not be flipped.

\dfrac{A - Cx}{A - C} REL \dfrac{D - B}{A - C}

Simplify.

x REL SOLUTION

Divide both sides by A - C. Because A - C is negative, the inequality sign REL must be flipped to FREL.

\dfrac{A - Cx}{A - C} FREL \dfrac{D - B}{A - C}

Simplify.

x FREL SOLUTION